Tuesday, September 24, 2013

I'm Trying to Get Inside Their Heads

In the latest Mathematics Teacher Journal from NCTM and Jaime Marts wrote in to Reader Reflections.  You can read what she wrote on page 84.  Anyway, her reflection is about making students thinking visible by placing questions around the room and having students respond to those questions.  And some of you are doing this too, so I've been seeing a lot of this lately.

So here are the posters I placed on tables around the room before we starting our outcome on solving equations:

We just finished learning about the properties, so I thought asking about the Inverse Property was appropriate.  I don't feel like the activity went over very well.  Most of the time the student stood around the poster talking about anything but math, until I walked up to them and asked what they were thinking.  

I had the students go to each poster twice so that they could see how their classmates responded to them.  Take a look at this.

I don't know why this is sideways, it's right-side-up when I go to upload it, sorry.  Anyway, see how little writing there is?  *Sigh*.  I know it's hard to see, but someone wrote "I don't know." and another person wrote "I agree."

For this class, there's more writing, but more irrelevant writing.  Someone wrote poems, then another person crossed them out, then the original person wrote back.

I know it's because it's the beginning of the year, but this is frustrating.  Either my questions aren't doing the trick, or the students need more practice with something like this, or some combination of both.  But I feel like this activity was a failure.  

Have you tried this?  How did it go for you?


  1. I am taking baby steps in this direction ... one question, time to think, then share with a partner ... and then share in class. If I tried the gallery walk with several questions I know I would get something similar as you did. I'm hoping after practicing for several weeks we can build up are thinking muscles to tackle more questions without prompting. I blogged about the question that gave my students difficulty ... it's much like these ... but just one: http://algebrasfriend.blogspot.com/2013/09/the-question-that-gave-them-pause.html.

  2. If you think this kind of thinking is important (I do, too), I'd encourage you to keep going in this direction. On a first attempt, they probably don't know what makes for a good answer to these questions. Maybe demonstrate (possibly again!) how you think about one of them, and then ask them to retry. The next go round (by which time they'll get theat you're serious about this) have them self-evaluate their answers or evaluate each other's. "Which two answers on the poster most thoroughly give their reasons in their response?" If you have the freedom to put a an item on a test like this, then they'll know that you really think it's important.

  3. Maybe try to reword the question. It seems they take the most literal and simple answer that technically does answer the question, but does not delve into the higher level thinking you are trying for. "When solving equations, why is it necessary to perform the same operation on both sides of the equation?" Hopefully that will eliminate the "so I can solve the equation." responses, since we have already established that I am solving the equation in the question.

  4. Try assigning a group to a question. At the end the group will go back and synthesize the answers given by their classmates into one answer, that they believe answers the question, to share with the class. It does two things: 1) It holds them responsible for really thinking about a question and coming up with the best answer that they can, and 2) there is a lot of peer pressure to stop the silly and off topic answers because it doesn't help the group formulate the answer.

    Another route into this is to start with an error analysis problem that gets at the heart of your question. For example, the solver forgot to use inverse operations on both sides. Ask the students to find the error, correct it, and then give a reason (besides so you get the right answer) why it's important not to make that error. It helps develop the critical thinking, but appears more as advise to their classmates to avoid errors.